Some Approaches to Symmetric Spaces

In this study we introduce some approaches , geometrical and algebraic which help to give further understanding of symmetric spaces and help scientists who are seeking for suitable spaces for their applications to carry on their job . One of the aims of this study is to put forward the close connection between different approaches to symmetric spaces , namely algebraic and geometrical features of these spaces with some results . Also giving some conclusions and remarks on the foundation of symmetric spaces with logical ordering of notions and consequences . We think that symmetric space is a very important field for understanding abstract and applied features of spaces , besides they are still need much effort to understand them because of the diversity of their approaches which mix between algebra and geometry , so this Paper is an attempt to disclose some of these features and helps in more understanding and put forward a base for future applications .